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Regular and Chaotic Dynamics

, Volume 17, Issue 6, pp 559–570 | Cite as

The problem of optimal control of a Chaplygin ball by internal rotors

  • Sergey BolotinEmail author
Article

Abstract

We study the problem of optimal control of a Chaplygin ball on a plane by means of 3 internal rotors. Using Pontryagin maximum principle, the equations of extremals are reduced to Hamiltonian equations in group variables. For a spherically symmetric ball, the solutions can be expressed in by elliptic functions.

Keywords

nonholonomic constraint vaconomic mechanics optimal control maximum principle Hamiltonian 

MSC2010 numbers

37J60 37J35 70E18 70F25 70H45 

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.University of Wisconsin-MadisonMadisonUSA
  2. 2.V.A. Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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